# 体积模量

（重定向自不可壓縮率

## 定义

${\displaystyle K=-V{\frac {\partial p}{\partial V}}}$

## 热力学关系

${\displaystyle K_{S}=\gamma \,p}$

${\displaystyle K_{T}=p\,}$

${\displaystyle c={\sqrt {\frac {K}{\rho }}}.}$

16×1010[1]

2.2×109[3]

## 参考文献

1. 钟锡华、周岳明. 《力学》. 北京大学出版社. 2000年12月: 204. ISBN 978-7-301-04591-6.
2. ^ Phys. Rev. B 32, 7988 - 7991 (1985), Calculation of bulk moduli of diamond and zinc-blende solids
3. ^ 存档副本. [2010-07-28]. （原始内容存档于2012-08-30）.
4. ^

${\displaystyle (\lambda ,\,G)}$  ${\displaystyle (E,\,G)}$  ${\displaystyle (K,\,\lambda )}$  ${\displaystyle (K,\,G)}$  ${\displaystyle (\lambda ,\,\nu )}$  ${\displaystyle (G,\,\nu )}$  ${\displaystyle (E,\,\nu )}$  ${\displaystyle (K,\,\nu )}$  ${\displaystyle (K,\,E)}$  ${\displaystyle (M,\,G)}$
${\displaystyle K=\,}$  ${\displaystyle \lambda +{\tfrac {2G}{3}}}$  ${\displaystyle {\tfrac {EG}{3(3G-E)}}}$  ${\displaystyle {\tfrac {\lambda (1+\nu )}{3\nu }}}$  ${\displaystyle {\tfrac {2G(1+\nu )}{3(1-2\nu )}}}$  ${\displaystyle {\tfrac {E}{3(1-2\nu )}}}$  ${\displaystyle M-{\tfrac {4G}{3}}}$
${\displaystyle E=\,}$  ${\displaystyle {\tfrac {G(3\lambda +2G)}{\lambda +G}}}$  ${\displaystyle {\tfrac {9K(K-\lambda )}{3K-\lambda }}}$  ${\displaystyle {\tfrac {9KG}{3K+G}}}$  ${\displaystyle {\tfrac {\lambda (1+\nu )(1-2\nu )}{\nu }}}$  ${\displaystyle 2G(1+\nu )\,}$  ${\displaystyle 3K(1-2\nu )\,}$  ${\displaystyle {\tfrac {G(3M-4G)}{M-G}}}$
${\displaystyle \lambda =\,}$  ${\displaystyle {\tfrac {G(E-2G)}{3G-E}}}$  ${\displaystyle K-{\tfrac {2G}{3}}}$  ${\displaystyle {\tfrac {2G\nu }{1-2\nu }}}$  ${\displaystyle {\tfrac {E\nu }{(1+\nu )(1-2\nu )}}}$  ${\displaystyle {\tfrac {3K\nu }{1+\nu }}}$  ${\displaystyle {\tfrac {3K(3K-E)}{9K-E}}}$  ${\displaystyle M-2G\,}$
${\displaystyle G=\,}$  ${\displaystyle {\tfrac {3(K-\lambda )}{2}}}$  ${\displaystyle {\tfrac {\lambda (1-2\nu )}{2\nu }}}$  ${\displaystyle {\tfrac {E}{2(1+\nu )}}}$  ${\displaystyle {\tfrac {3K(1-2\nu )}{2(1+\nu )}}}$  ${\displaystyle {\tfrac {3KE}{9K-E}}}$
${\displaystyle \nu =\,}$  ${\displaystyle {\tfrac {\lambda }{2(\lambda +G)}}}$  ${\displaystyle {\tfrac {E}{2G}}-1}$  ${\displaystyle {\tfrac {\lambda }{3K-\lambda }}}$  ${\displaystyle {\tfrac {3K-2G}{2(3K+G)}}}$  ${\displaystyle {\tfrac {3K-E}{6K}}}$  ${\displaystyle {\tfrac {M-2G}{2M-2G}}}$
${\displaystyle M=\,}$  ${\displaystyle \lambda +2G\,}$  ${\displaystyle {\tfrac {G(4G-E)}{3G-E}}}$  ${\displaystyle 3K-2\lambda \,}$  ${\displaystyle K+{\tfrac {4G}{3}}}$  ${\displaystyle {\tfrac {\lambda (1-\nu )}{\nu }}}$  ${\displaystyle {\tfrac {2G(1-\nu )}{1-2\nu }}}$  ${\displaystyle {\tfrac {E(1-\nu )}{(1+\nu )(1-2\nu )}}}$  ${\displaystyle {\tfrac {3K(1-\nu )}{1+\nu }}}$  ${\displaystyle {\tfrac {3K(3K+E)}{9K-E}}}$